Extremum properties of the new ellipsoid
Extremum properties of the new ellipsoid
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DOI：
10.5556/j.tkjm.38.2007.86
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发表时间：
2007-06
影响因子：
0.6
通讯作者：
Yuan Jun;Si Lin;G. Leng
中科院分区：
文献类型：
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作者：
Yuan Jun;Si Lin;G. Leng
For a convex body K in R(superscript n), Lutwak, Yang and Zhang defined a new ellipsoid Γ(subscript -2)K, which is the dual analog of the Legendre ellipsoid. In this paper, we prove the following two results: (ⅰ) For any origin-symmetric convex body K, there exist an ellipsoid E and a parallelotope P such that Γ(subscript -2)E⊇Γ(subscript -2)K⊇Γ(subscript -2)P and V(E)=V(K)=V(P); (ⅱ) For any convex body K whose John point is at the origin, then there exists a simplex T such that Γ(subscript -2)K⊇Γ(subscript -2)T and V(K)=V(T).
